Question 1: Given a point (3, 4) and a gradient m = 2, write the equation of the line using y - y₁ = m(x - x₁).

Answer: y - 4 = 2(x - 3)

Question 2: For the point (0, 5) and gradient m = -1, find the equation of the line.

Answer: y - 5 = -1(x - 0) or y = -x + 5

Question 3: Using point (2, -3) and gradient m = 0.5, form the equation of the line.

Answer: y + 3 = 0.5(x - 2)

Question 1: A line passes through (1, 2) and has a gradient of 3. Write its equation.

Answer: y - 2 = 3(x - 1)

Question 2: Find the equation of a line passing through (4, 1) with gradient -2.

Answer: y - 1 = -2(x - 4)

Question 3: Write the equation of the line through point (0, 0) with gradient m = 4.

Answer: y - 0 = 4(x - 0) or y = 4x

Question 1: A line passes through the points (2, 3) and (5, 11). Find the gradient and write the equation of the line using y - y₁ = m(x - x₁).

Answer: Gradient m = (11 - 3) / (5 - 2) = 8/3; Equation: y - 3 = (8/3)(x - 2)

Question 2: A cyclist starts at point (0, 0). If her path has a gradient of 1.5 and she passes through (4, y), find y and write the equation of her route.

Answer: y - 0 = 1.5(4 - 0) => y = 6; Equation: y - 0 = 1.5(x - 0)

Question 1: A car is traveling along a straight road. Its distance from a starting point (measured in km) can be modeled by a line passing through (0, 0) with a gradient of 0.8. Write the equation describing its distance after x hours.

Answer: Distance = 0.8x

Question 2: A factory produces 150 units of a product per day. The production level over time (days) can be described by the line passing through (0, 150) with a gradient of 20 units per day. Write the equation for production after x days.

Answer: Production = 20x + 150

Question 1: Find the equation of a line that passes through (2, -1) and (6, 7). Use y - y₁ = m(x - x₁).

Answer: Gradient m = (7 + 1) / (6 - 2) = 8/4 = 2; Equation: y + 1 = 2(x - 2)

Question 2: A line has equation y - 5 = -0.5(x - 4). Find the coordinates of the point where it crosses the y-axis.

Answer: Set x=0: y - 5 = -0.5(0 - 4) => y - 5 = 2 => y=7; Crossing point (0,7)

Question 1: A student writes the equation y - 3 = 4(x + 2). Identify and correct the mistake if the line passes through (1, 7).

Answer: The correct equation should be y - 7 = 4(x - 1) because the point is (1,7).

Question 2: A line passes through (0, 0) with gradient 3. A student mistakenly writes y - 0 = 3(x + 2). Explain the mistake and provide the correct equation.

Answer: The mistake is adding + 2 inside the brackets; it should be y - 0 = 3(x - 0) or y=3x.